Geometric phase effects [1]}, [2]} are fundamentally
important in understanding electrical transport property in
quantum Hall effect [3]}, [4]},
anomalous Hall effect[5]}, [6]}, and anomalous thermoelectric
transport [7]}. It is successful in characterizing the underlying
mechanism of quantum spin Hall effect [8]}, [9]}.
Such an elegant connection between mathematics and physics
provides a broad and deep understanding of basic material properties.
Although there is a quite difference between phonons and electrons, we still
can use the topological description to study the underlying
properties of the phonon transport, such as topological phonon
modes in dynamic instability of microtubules [10]} and in filamentary structures
[11]}, Berry-phase-induced
heat pumping [12]}, and the Berry-phase contribution of
molecular vibrational instability [13]}.
